Governments worldwide subsidize fishing industries to the tune of $15 billion a year
See here and here, among many, many others.
Why do you think extensive fishing can continue when the supply is drying up? In a free market, fisheries and fishermen would be going out of business, and the price of fish would be skyrocketing. Not happening though, is it?
We could also bring in the failure of the concept of "public" resources, too, but that's a whole different subject.
Nice try, though. Don't teach your grandma how to suck eggs.